To put it another way the event is an all or nothing processes. The ionizing radiation ( charged particles or photon) produces ion pairs in the tube.The high voltage between the anode and cathode accelerated the electrons in the gas of the tube which in tern causes more ionization which can initiate an "avalanche" of ions creating pulse of charge at the anode. GM counter do not discriminate between type of radiation. A pulse is created every time enough ion pairs are left behind in the tube.
If the tube voltage is reduce enough you get a range of voltages where you can get a pulse created that is proportional to the energy deposited in the gas. This is the basis of the proportional counter. Reducing the tube voltage further the the output of the chamber again becomes independent of the energy for the most part. This then becomes and ionization chamber.
Each of the three types of detectors above are basically the same with a conducting cylinder enclosing a wire on the axis with a positive voltage on the wire. However the actual construction, size, and gas used varies with the chambers and use.